Re: Cube root of -1 and 1

• To: mathgroup at smc.vnet.net
• Subject: [mg90896] Re: Cube root of -1 and 1
• From: lehin.p at gmail.com
• Date: Mon, 28 Jul 2008 07:54:21 -0400 (EDT)
• References: <g6h5fm\$h26\$1@smc.vnet.net>

```On 27 =C9=C0=CC, 10:44, Bob F <deepyog... at gmail.com> wrote:
> Could someone explain why Mathematica evaluates these so differently?
>
> In[53]:=
>
> (Sqrt[36] - 7)^(1/3)
> (Sqrt[36] - 5)^(1/3)
>
> Out[53]= (-1)^(1/3)
>
> Out[54]= 1
>
> In other words why isn't (-1)^1/3 expressed as -1 ??
>
> Thanks...
>
> -Bob

I subscribe to the question. I also do not understand this behavour:

In[12]:= (-1)^(1/3)//ComplexExpand
Out[12]= 1/2+(I Sqrt[3])/2

In[13]:= FullSimplify[(-1)^(1/3) == 1/2 + (I Sqrt[3])/2]
Out[13]= True

But:

In[14]:= FullSimplify[(-1)^(1/3)==-1]
Out[14]= False

In[17]:= (-1)^3
Out[17]= -1

In[20]:= FullSimplify[(-1)^3 == -1]
Out[20]= True

It is contradiction, is not it?

```

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